Add two numbers represented by linked lists

Given two numbers represented by two lists, write a function that returns the sum list. The sum list is list representation of the addition of two input numbers.

Example:

Input:
List1: 5->6->3 // represents number 365
List2: 8->4->2 // represents number 248
Output:
Resultant list: 3->1->6 // represents number 613
Explanation: 365 + 248 = 613
Input:
List1: 7->5->9->4->6 // represents number 64957
List2: 8->4 // represents number 48
Output:
Resultant list: 5->0->0->5->6 // represents number 65005
Explanation: 64957 + 48 = 65005

Approach: Traverse both lists and One by one pick nodes of both lists and add the values. If the sum is more than 10 then make carry as 1 and reduce sum. If one list has more elements than the other then consider remaining values of this list as 0.

The steps are:

Traverse the two linked lists from start to end
Add the two digits each from respective linked lists.
If one of the list has reached the end then take 0 as its digit.
Continue it until both the lists end.
If the sum of two digits is greater than 9 then set carry as 1 and the current digit as sum % 10

Below is the implementation of this approach.

C++

// C++ program to add two numbers
// represented by linked list
#include <bits/stdc++.h>
using namespace std;
 
/* Linked list node */
class Node {
public:
    int data;
    Node* next;
};
 
/* Function to create a 
new node with given data */
Node* newNode(int data)
{
    Node* new_node = new Node();
    new_node->data = data;
    new_node->next = NULL;
    return new_node;
}
 
/* Function to insert a node at the
beginning of the Singly Linked List */
void push(Node** head_ref, int new_data)
{
    /* allocate node */
    Node* new_node = newNode(new_data);
 
    /* link the old list off the new node */
    new_node->next = (*head_ref);
 
    /* move the head to point to the new node */
    (*head_ref) = new_node;
}
 
/* Adds contents of two linked lists and 
return the head node of resultant list */
Node* addTwoLists(Node* first, Node* second)
{
 
    // res is head node of the resultant list
    Node* res = NULL;
    Node *temp, *prev = NULL;
    int carry = 0, sum;
 
    // while both lists exist
    while (first != NULL
           || second != NULL) {
        // Calculate value of next
        // digit in resultant list.
        // The next digit is sum of
        // following things
        // (i) Carry
        // (ii) Next digit of first
        // list (if there is a next digit)
        // (ii) Next digit of second
        // list (if there is a next digit)
        sum = carry + (first ? first->data : 0)
              + (second ? second->data : 0);
 
        // update carry for next calulation
        carry = (sum >= 10) ? 1 : 0;
 
        // update sum if it is greater than 10
        sum = sum % 10;
 
        // Create a new node with sum as data
        temp = newNode(sum);
 
        // if this is the first node then
        // set it as head of the resultant list
        if (res == NULL)
            res = temp;
 
        // If this is not the first
        // node then connect it to the rest.
        else
            prev->next = temp;
 
        // Set prev for next insertion
        prev = temp;
 
        // Move first and second
        // pointers to next nodes
        if (first)
            first = first->next;
        if (second)
            second = second->next;
    }
 
    if (carry > 0)
        temp->next = newNode(carry);
 
    // return head of the resultant list
    return res;
}
 
// A utility function to print a linked list
void printList(Node* node)
{
    while (node != NULL) {
        cout << node->data << " ";
        node = node->next;
    }
    cout << endl;
}
 
/* Driver code */
int main(void)
{
    Node* res = NULL;
    Node* first = NULL;
    Node* second = NULL;
 
    // create first list 7->5->9->4->6
    push(&first, 6);
    push(&first, 4);
    push(&first, 9);
    push(&first, 5);
    push(&first, 7);
    printf("First List is ");
    printList(first);
 
    // create second list 8->4
    push(&second, 4);
    push(&second, 8);
    cout << "Second List is ";
    printList(second);
 
    // Add the two lists and see result
    res = addTwoLists(first, second);
    cout << "Resultant list is ";
    printList(res);
 
    return 0;
}
 
// This code is contributed by rathbhupendra

C

#include <stdio.h>
#include <stdlib.h>
 
/* Linked list node */
struct Node {
    int data;
    struct Node* next;
};
 
/* Function to create a new node with given data */
struct Node* newNode(int data)
{
    struct Node* new_node
        = (struct Node*)malloc(sizeof(struct Node));
    new_node->data = data;
    new_node->next = NULL;
    return new_node;
}
 
/* Function to insert a node
at the beginning of the Singly Linked List */
void push(struct Node** head_ref, int new_data)
{
    /* allocate node */
    struct Node* new_node = newNode(new_data);
 
    /* link the old list off the new node */
    new_node->next = (*head_ref);
 
    /* move the head to point to the new node */
    (*head_ref) = new_node;
}
 
/* Adds contents of two linked
 lists and return the head node
 of resultant list */
struct Node* addTwoLists(struct Node* first,
                         struct Node* second)
{
 
    // res is head node of the resultant list
    struct Node* res = NULL;
    struct Node *temp, *prev = NULL;
    int carry = 0, sum;
 
    // while both lists exist
    while (first != NULL || second != NULL) {
        // Calculate value of next
        // digit in resultant list.
        // The next digit is sum
        // of following things
        // (i)  Carry
        // (ii) Next digit of first
        // list (if there is a next digit)
        // (ii) Next digit of second
        // list (if there is a next digit)
        sum = carry + (first ? first->data : 0)
              + (second ? second->data : 0);
 
        // Update carry for next calulation
        carry = (sum >= 10) ? 1 : 0;
 
        // Update sum if it is greater than 10
        sum = sum % 10;
 
        // Create a new node with sum as data
        temp = newNode(sum);
 
        // if this is the first node then
        // set it as head of the resultant list
        if (res == NULL)
            res = temp;
        // If this is not the first node
        // then connect it to the rest.
        else
            prev->next = temp;
 
        // Set prev for next insertion
        prev = temp;
 
        // Move first and second
        // pointers to next nodes
        if (first)
            first = first->next;
        if (second)
            second = second->next;
    }
 
    if (carry > 0)
        temp->next = newNode(carry);
 
    // return head of the resultant list
    return res;
}
 
// A utility function to print a linked list
void printList(struct Node* node)
{
    while (node != NULL) {
        printf("%d ", node->data);
        node = node->next;
    }
    printf("\n");
}
 
/* Driver code */
int main(void)
{
    struct Node* res = NULL;
    struct Node* first = NULL;
    struct Node* second = NULL;
 
    // create first list 7->5->9->4->6
    push(&first, 6);
    push(&first, 4);
    push(&first, 9);
    push(&first, 5);
    push(&first, 7);
    printf("First List is ");
    printList(first);
 
    // create second list 8->4
    push(&second, 4);
    push(&second, 8);
    printf("Second List is ");
    printList(second);
 
    // Add the two lists and see result
    res = addTwoLists(first, second);
    printf("Resultant list is ");
    printList(res);
 
    return 0;
}

Java

// Java program to add two numbers
// represented by linked list
 
class LinkedList {
 
    static Node head1, head2;
 
    static class Node {
 
        int data;
        Node next;
 
        Node(int d)
        {
            data = d;
            next = null;
        }
    }
 
    /* Adds contents of two linked
lists and return the head node
of resultant list */
    Node addTwoLists(Node first, Node second)
    {
        // res is head node of the resultant list
        Node res = null;
        Node prev = null;
        Node temp = null;
        int carry = 0, sum;
 
        // while both lists exist
        while (first != null || second != null) {
            // Calculate value of next
            // digit in resultant list.
            // The next digit is sum
            // of following things
            // (i)  Carry
            // (ii) Next digit of first
            // list (if there is a next digit)
            // (ii) Next digit of second
            // list (if there is a next digit)
            sum = carry + (first != null ? first.data : 0)
                  + (second != null ? second.data : 0);
 
            // update carry for next calulation
            carry = (sum >= 10) ? 1 : 0;
 
            // update sum if it is greater than 10
            sum = sum % 10;
 
            // Create a new node with sum as data
            temp = new Node(sum);
 
            // if this is the first node then set
            // it as head of the resultant list
            if (res == null) {
                res = temp;
            }
 
            // If this is not the first
            // node then connect it to the rest.
            else {
                prev.next = temp;
            }
 
            // Set prev for next insertion
            prev = temp;
 
            // Move first and second pointers
            // to next nodes
            if (first != null) {
                first = first.next;
            }
            if (second != null) {
                second = second.next;
            }
        }
 
        if (carry > 0) {
            temp.next = new Node(carry);
        }
 
        // return head of the resultant list
        return res;
    }
    /* Utility function to print a linked list */
 
    void printList(Node head)
    {
        while (head != null) {
            System.out.print(head.data + " ");
            head = head.next;
        }
        System.out.println("");
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        LinkedList list = new LinkedList();
 
        // creating first list
        list.head1 = new Node(7);
        list.head1.next = new Node(5);
        list.head1.next.next = new Node(9);
        list.head1.next.next.next = new Node(4);
        list.head1.next.next.next.next = new Node(6);
        System.out.print("First List is ");
        list.printList(head1);
 
        // creating seconnd list
        list.head2 = new Node(8);
        list.head2.next = new Node(4);
        System.out.print("Second List is ");
        list.printList(head2);
 
        // add the two lists and see the result
        Node rs = list.addTwoLists(head1, head2);
        System.out.print("Resultant List is ");
        list.printList(rs);
    }
}
 
// this code has been contributed by Mayank Jaiswal

Python

# Python program to add two numbers represented by linked list
 
# Node class
 
 
class Node:
 
    # Constructor to initialize the node object
    def __init__(self, data):
        self.data = data
        self.next = None
 
 
class LinkedList:
 
    # Function to initialize head
    def __init__(self):
        self.head = None
 
    # Function to insert a new node at the beginning
    def push(self, new_data):
        new_node = Node(new_data)
        new_node.next = self.head
        self.head = new_node
 
    # Add contents of two linked lists and return the head
    # node of resultant list
    def addTwoLists(self, first, second):
        prev = None
        temp = None
        carry = 0
 
        # While both list exists
        while(first is not None or second is not None):
 
            # Calculate the value of next digit in
            # resultant list
            # The next digit is sum of following things
            # (i) Carry
            # (ii) Next digit of first list (if ther is a
            # next digit)
            # (iii) Next digit of second list ( if there
            # is a next digit)
            fdata = 0 if first is None else first.data
            sdata = 0 if second is None else second.data
            Sum = carry + fdata + sdata
 
            # update carry for next calculation
            carry = 1 if Sum >= 10 else 0
 
            # update sum if it is greater than 10
            Sum = Sum if Sum < 10 else Sum % 10
 
            # Create a new node with sum as data
            temp = Node(Sum)
 
            # if this is the first node then set it as head
            # of resultant list
            if self.head is None:
                self.head = temp
            else:
                prev.next = temp
 
            # Set prev for next insertion
            prev = temp
 
            # Move first and second pointers to next nodes
            if first is not None:
                first = first.next
            if second is not None:
                second = second.next
 
        if carry > 0:
            temp.next = Node(carry)
 
    # Utility function to print the linked LinkedList
    def printList(self):
        temp = self.head
        while(temp):
            print temp.data,
            temp = temp.next
 
 
# Driver code
first = LinkedList()
second = LinkedList()
 
# Create first list
first.push(6)
first.push(4)
first.push(9)
first.push(5)
first.push(7)
print "First List is ",
first.printList()
 
# Create second list
second.push(4)
second.push(8)
print "\nSecond List is ",
second.printList()
 
# Add the two lists and see result
res = LinkedList()
res.addTwoLists(first.head, second.head)
print "\nResultant list is ",
res.printList()
 
# This code is contributed by Nikhil Kumar Singh(nickzuck_007)

C#

// C# program to add two numbers
// represented by linked list
using System;
 
public class LinkedList {
 
    Node head1, head2;
 
    public class Node {
        public int data;
        public Node next;
 
        public Node(int d)
        {
            data = d;
            next = null;
        }
    }
 
    /* Adds contents of two linked lists
    and return the head node of resultant list */
    Node addTwoLists(Node first, Node second)
    {
        // res is head node of the resultant list
        Node res = null;
        Node prev = null;
        Node temp = null;
        int carry = 0, sum;
 
        // while both lists exist
        while (first != null || second != null) {
            // Calculate value of next digit in resultant
            // list. The next digit is sum of following
            // things (i) Carry (ii) Next digit of first
            // list (if there is a next digit) (ii) Next
            // digit of second list (if there is a next
            // digit)
            sum = carry + (first != null ? first.data : 0)
                  + (second != null ? second.data : 0);
 
            // update carry for next calulation
            carry = (sum >= 10) ? 1 : 0;
 
            // update sum if it is greater than 10
            sum = sum % 10;
 
            // Create a new node with sum as data
            temp = new Node(sum);
 
            // if this is the first node then set it as head
            // of the resultant list
            if (res == null) {
                res = temp;
            }
 
            // If this is not the first
            // node then connect it to the rest.
            else {
                prev.next = temp;
            }
 
            // Set prev for next insertion
            prev = temp;
 
            // Move first and second pointers to next nodes
            if (first != null) {
                first = first.next;
            }
            if (second != null) {
                second = second.next;
            }
        }
 
        if (carry > 0) {
            temp.next = new Node(carry);
        }
 
        // return head of the resultant list
        return res;
    }
    /* Utility function to print a linked list */
 
    void printList(Node head)
    {
        while (head != null) {
            Console.Write(head.data + " ");
            head = head.next;
        }
        Console.WriteLine("");
    }
 
    // Driver code
    public static void Main(String[] args)
    {
        LinkedList list = new LinkedList();
 
        // creating first list
        list.head1 = new Node(7);
        list.head1.next = new Node(5);
        list.head1.next.next = new Node(9);
        list.head1.next.next.next = new Node(4);
        list.head1.next.next.next.next = new Node(6);
        Console.Write("First List is ");
        list.printList(list.head1);
 
        // creating seconnd list
        list.head2 = new Node(8);
        list.head2.next = new Node(4);
        Console.Write("Second List is ");
        list.printList(list.head2);
 
        // add the two lists and see the result
        Node rs = list.addTwoLists(list.head1, list.head2);
        Console.Write("Resultant List is ");
        list.printList(rs);
    }
}
 
// This code contributed by Rajput-Ji

Output

First List is 7 5 9 4 6 
Second List is 8 4 
Resultant list is 5 0 0 5 6

Complexity Analysis:

Time Complexity: O(m + n), where m and n are number of nodes in first and second lists respectively.
The lists needs to be traversed only once.
Space Complexity: O(m + n).
A temporary linked list is needed to store the output number

https://www.youtube.com/watch?v=LLPuC5kWD8U

Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem.

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My Personal Notes

Add two numbers represented by linked lists | Set 1

C++

C

Java

Python

C#

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